Column I Column II (a) Let \( f(x)=\sqrt{\log (\cos [\{x\}])} \), t...

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Column I
Column II
(a) Let \( f(x)=\sqrt{\log (\cos [\{x\}])} \), then \( f(x) \) is
(p) Even and Periodic function
P
(b) Let \( f:(-1,1) \rightarrow R \) be defined as
(q) Bounded
W \( f(x)=\sum_{r=1}^{100}\left[x^{2 r}\right] \) then \( f(x) \) is
(c) Let \( f(x)=\cos ^{-1}\left(\left[e^{x}\right]-1\right)+\sin ^{-1}\left(\left[e^{x}\right]\right) \)
(r) Domain contains at least one then \( f(x) \) is integer and atmost 3 integers
(s) Both many one and odd function
[Note \( :[y] \) and \( \{y\} \) denote greatest integer and fractional part function of \( y \) respectively.]
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